3 Answers
3

Simple answer -- there are twelve terms of request in a normal year (chaim, shalom, sason, simcha ...), one for each month. Leap year has a thirteenth month, so a thirteenth term. Now why we say "indemnity of iniquity" [try saying that five times fast!] per se (other than it follows nicely from the previous pair about forgiveness and pardon), and whether given phrases map to specific months or if it's 12=12, I don't know. Though I assume that "pasha" is the most severe form of sin, so it's reasonable that we don't push our luck and thus only ask for forgiveness for it every few years.

The three expressions for different types of sin are used widely (e.g. on every Yom Kippur), פשע and חטא, עון . Sometimes חטא is used as a generic form but otherwise all three occur together. It is inconceivable that this form of sin can only be atoned during this restricted period, so why is it left out during normal years?
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Avrohom YitzchokDec 26 '11 at 9:26

I just found a Kunteros Achron #448 published on the bottom of the Taamei Haminhagim #448. He writes that the reason we say Ulichaporas Pasha is in case the year was made into a leap year in error and through that we are eating Chomeitz on Pesach.

A thought that I had today. The main purpose of Rosh Chodesh according to what we say in Mussaf is "Roshei Chadosim L'Amcha Nosato, Zman Kaporo Lchol Toldosom" and this is reaffirmed when we have an additional 13th month by saying Ulichaporas Pesha. There are those that say Slichos Yom Kippur Kotton Erev Rosh Chodesh to have a Kaporo for the entire previous month.